Niccolo Machiavelli, perhaps the shrewdest political philosopher in history, believed that great events were shaped by luck — or “fortuna,” as he called this unpredictable force of life. The same actions might produce success or failure, depending on the whims of the goddess Fortuna.

You wouldn’t know it by listening to gloomy commentators, but the United States has been extremely lucky of late. Its inherent economic strength has become more obvious. Meanwhile, its adversaries have suffered reversals — some of their own making, others because of bad luck.

With this advantageous position, the United States can afford to think like a superpower. It shouldn’t rush to make concessions to weaker nations or to gain agreements that aren’t fully ripe, as may be the case with nuclear talks with Iran. It shouldn’t be shy about helping its friends or making its adversaries pay for their reckless behavior, as in dealing with Russia’s aggression in Ukraine.

It’s a diabolical piece of luck, too, that the Islamic State, which poses a deadly threat in Syria and Iraq, has taken the hideous action of burning alive a Jordanian Muslim pilot. Millions of Arabs are outraged and calling for revenge. With this death-cult action, the extremists have done more to undermine their standing than a thousand U.S. bombing raids or a million State Department propaganda tweets could have accomplished.

Americans are always asking why Arabs don’t denounce atrocities committed in the name of Islam. Well, it’s happening now. “Barbarity,” screams the headline in the London-based Arabic newspaper Al-Hayat. “Vicious,” says the emir of Kuwait. A “brutal, heinous crime,” says Saudi Arabia. The United States shouldn’t raise its voice louder than the indignant Muslim world. Restrain the rhetoric; use force invisibly; act like a superpower.

To understand the current “correlation of forces,” as the Russians like to say, let’s look at some evidence about American economic power gathered by Goldman Sachs last month in a report titled “U.S. Preeminence.”

First, GDP growth: From the peak before the 2008 financial crisis, the U.S. economy has grown a further 8.1 percent in real terms, compared with declines of 2.2 percent for the euro zone and 1.1 percent for Japan. The gap between GDP growth rates in fast-rising emerging-market economies and the United States shrank from 6.5 percentage points in 2007 to 2.6 points in 2014, and it’s expected to narrow further this year to 1.2 points as China slows.